Log In Start studying!

Select your language

Suggested languages for you:
Deutsch (DE)
Deutsch (UK)
Deutsch (US)

Americas

Europe

Answers without the blur. Sign up and see all textbooks for free! → Illustration

Chapter 5: Induction and Recursion

Expert-verified
Discrete Mathematics and its Applications
Pages: 311 - 379
Discrete Mathematics and its Applications

Discrete Mathematics and its Applications

Book edition 7th
Author(s) Kenneth H. Rosen
Pages 808 pages
ISBN 9780073383095

Answers without the blur.

Just sign up for free and you're in.

Register for Free I’ll do it later
Illustration

284 Questions for Chapter 5: Induction and Recursion

  1. Assume that a chocolate bar consists of n squares arranged in a rectangular pattern. The entire bar, a smaller rectangular piece of the bar, can be broken along a vertical or a horizontal line separating the squares. Assuming that only one piece can be broken at a time, determine how many breaks you must successfully make to break the bar into n separate squares. Use strong induction to prove your answer

    Found on Page 342

  2. a) Find a formula for

    Found on Page 330

  3. Give a recursive definition of Sm(n), the sum of the integer m and the non negative integer n.

    Found on Page 358

  4. Give a recursive algorithm for finding the maximum of a finite set of integers, making use of the fact that the maximum of n integers is the larger of the last integer in the list and the maximum of the first n - 1 integers in the list.

    Found on Page 370

  5. a) Give a recursive definition of the length of a string.

    Found on Page 378

  6. Use mathematical induction to prove that \(9\) divides \({n^3} + {\left( {n + 1} \right)^3} + {\left( {n + 2} \right)^3}\) whenever \(n\)is a nonnegative integer.

    Found on Page 379

  7. Give a recursive algorithm for finding the minimum of a finite set of integers, making use of the fact that the maximum of n integers is the smaller of the last integer in the list and the minimum of the first n - 1 integers in the list.

    Found on Page 370

  8. Suppose that both the program assertionp{S}q0and the conditional statementq0→q1are true. Show thatp{S}q1also must be true.

    Found on Page 377

  9. Consider this variation of the game of Nim. The game begins with n matches. Two players take turns removing matches, one, two, or three at a time. The player removing the last match loses. Using strong induction to show that if each player plays the best strategy possible, the first player wins ifn=4j,4j+2, or4j+3 for some nonnegative integer jand the second player wins in the remaining case whenn=4j+1 for some nonnegative integer j.

    Found on Page 342

  10. (a) Find the formula for 12+14+18+⋯+12n by examining the values of this expression for small values of n.

    Found on Page 330

Related Math Textbooks with Solutions

View all the textbook solutions in Math

94% of StudySmarter users get better grades.

Sign up for free
94% of StudySmarter users get better grades.